Overload List
| # | Signature | Description |
|---|---|---|
| 1 | procedure InverseGaussianCDFInv(const P: TDenseMtxVec; Mu: Double; Lambda: Double; const Res: TDenseMtxVec); | Inverse Gaussian distribution PPF (vectorized). |
| 2 | function InverseGaussianCDFInv(p: Double; Mu: Double; Lambda: Double): Double; | Inverse Gaussian (Wald) percent point function (PPF, quantile / inverse CDF). |
Overload 1: procedure InverseGaussianCDFInv(const P: TDenseMtxVec; Mu: Double; Lambda: Double; const Res: TDenseMtxVec);
Inverse Gaussian distribution PPF (vectorized).
| # | Name | Description |
|---|---|---|
| 1 | P | Defines distribution probabilities, real vector or matrix with values within closed interval [0,1]. |
| 2 | Mu | Defines distribution Mu parameter. Mu must be a positive scalar. |
| 3 | Lambda | Defines distribution Lambda parameter. Lambda must be a positive scalar. |
| 4 | Res | After calculation stores the PPF calculated from P, Mu and Lambda. Length and Complex properties of Res are adjusted automatically to match Length and Complex properties of P. |
Result: stored in self (calling object)
Overload 2: function InverseGaussianCDFInv(p: Double; Mu: Double; Lambda: Double): Double;
Inverse Gaussian (Wald) percent point function (PPF, quantile / inverse CDF).
| # | Name | Description |
|---|---|---|
| 1 | p | Probability, real value on the closed interval [0,1]. |
| 2 | Mu | Distribution mean parameter. Mu must be a positive scalar (Mu>0). |
| 3 | Lambda | Distribution shape parameter. Lambda must be a positive scalar (Lambda>0). |
Returns: Double - the value x such that InverseGaussianCDF(x,Mu,Lambda)=p. Computed by bisection of the CDF on [SQRTEPS, 1e8]. Probability p must lie on [0,1] and Mu, Lambda must both be positive, otherwise the result is NaN.
The percent point function is the inverse of the cumulative distribution function:
CDFInv(p | mu,lambda) = F^(-1)(p | mu,lambda) where F(x | mu,lambda) = p .
The inverse Gaussian CDF has no simple closed-form inverse; the result is obtained by numerically inverting the CDF with a bisection method (tolerance SQRTEPS). Returns NaN for p outside [0,1], Mu<=0 or Lambda<=0.